The question is from Permutation and Combination. A question which combines probability with progression. Our task is to identify the infinite series which is ultimately the probability of that given event. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 14: A and B take part in a duel. A can strike with an accuracy of 0.6. B can strike with an accuracy of 0.8. A has the first shot, post which they strike alternately. What is the probability that A wins the duel?

- \\frac{7}{10}\\)
- \\frac{15}{23}\\)
- \\frac{2}{3}\\)
- \\frac{11}{17}\\)

Valid until 28th Sep

Online Batches Available Now!

A can win in the following scenarios:

A strikes in first shot.

A misses in the first shot, B misses in the second, A strikes in the third.

A misses in the 1st shot, B misses in the 2nd, A misses the 3rd, B misses the 4th and A strikes the 5th.

*And so on…*

P(A in 1^{st} shot) = 0.6

P(A in 3^{rd} shot) = 0.4 * 0.2 * 0.6 {A misses, then B misses and then A strikes}

P(A in 5^{st} shot) = 0.4 * 0.2 * 0.4 * 0.2 * 0.6 {A misses, then B misses and then A misses, then B misses, then A strikes}

Overall probability = Sum of all these

= 0.6 + 0.4 * 0.2 * 0.6 + 0.4 * 0.2 * 0.4 * 0.2 * 0.6 + …

Which is nothing but

0.6 + (0.4 * 0.2) * 0.6 + (0.4 * 0.2)^{2} * 0.6 + (0.4 * 0.2)^{3} * 0.6…

This is an infinite geometric progression with first term 0.6 and common ratio 0.4 * 0.2

Required Probability = \\frac{a}{1 - r}\\) = \\frac{0.6}{1 - 0.08}\\) = \\frac{0.6}{0.92}\\) = \\frac{30}{46}\\) = \\frac{15}{23}\\)

The question is **"What is the probability that A wins the duel?"**

Choice B is the correct answer.

CAT 2021

Enroll at

44,000/-

Online Classroom Batches Starting Now!

1. Digit Numbers | CAT Permutation and Combination | CAT Coaching Online

2. Numbers with Distinct Digits | CAT Permutation and Combination | CAT Coaching Online

3. Alphabetical Order | CAT Permutation and Combination | CAT Coaching Online

4. Geometric Progression | CAT Permutation and Combination | CAT Coaching Online

5. Bayes Theorem | CAT Permutation and Combination | CAT Coaching Online

2. Numbers with Distinct Digits | CAT Permutation and Combination | CAT Coaching Online

3. Alphabetical Order | CAT Permutation and Combination | CAT Coaching Online

4. Geometric Progression | CAT Permutation and Combination | CAT Coaching Online

5. Bayes Theorem | CAT Permutation and Combination | CAT Coaching Online

6. Rearranging Letters | CAT Permutation and Combination | CAT Coaching Online

7. Possible Integer Solutions | CAT Permutation and Combination | CAT Coaching Online

8. Rearrangement of Letters | CAT Permutation and Combination | CAT Coaching Online

9. Number Theory | CAT Permutation and Combination | CAT Coaching Online

10. Distribution | CAT Permutation and Combination | CAT Coaching Online

7. Possible Integer Solutions | CAT Permutation and Combination | CAT Coaching Online

8. Rearrangement of Letters | CAT Permutation and Combination | CAT Coaching Online

9. Number Theory | CAT Permutation and Combination | CAT Coaching Online

10. Distribution | CAT Permutation and Combination | CAT Coaching Online

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com